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# Trigonometry 2

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### Trigonometry 2

1. 1. Trigonometry
2. 2. Lesson Objectives <ul><li>Calculate the value of angles in a right angled triangle using trigonometric ratios. </li></ul><ul><li>Apply trigonometry to perform calculation checks. </li></ul><ul><li>Calculate the length of a side in a right angled triangle using trigonometric ratios. </li></ul>
3. 3. Trigonometric Ratios <ul><li>SOHCAHTOA </li></ul><ul><li>Sine Ɵ = opposite__ </li></ul><ul><li> hypotenuse </li></ul><ul><li>Cosine Ɵ = adjacent__ </li></ul><ul><li> hypotenuse </li></ul><ul><li>Tangent Ɵ = opposite </li></ul><ul><li> adjacent </li></ul>
4. 4. Example 2 <ul><li>Find the value of angles Ɵ and λ in triangle LMN. </li></ul><ul><li> </li></ul>13m 12m 5m θ λ
5. 5. Example 2 <ul><li>Sin Ɵ = Opp = 12 = 0.923 </li></ul><ul><li> Hyp 13 </li></ul><ul><li>Ɵ = Sinˉ¹0.923 </li></ul><ul><li>Ɵ = 67.38º </li></ul><ul><li>Sin λ = Opp = 5 = 0.385 </li></ul><ul><li> Hyp 13 </li></ul><ul><li> λ = 22.62º </li></ul>
6. 6. Trigonometry Check <ul><li>Check:180º - 90° - 67.38° = 22.62° </li></ul><ul><li>Sin λ = 22.62° </li></ul><ul><li>Cos λ = 12 = 0.923 Cos λ = 22.62° </li></ul><ul><li> 13 </li></ul><ul><li>Tan λ = 5 = 0.416 Tan λ = 22.62° </li></ul><ul><li> 12 </li></ul>
7. 7. Example 3 <ul><li>Find the value of angles QPR and RQP and the length of the side PR. </li></ul>7m 6m Q P R
8. 8. Example 3 <ul><li>Find angle QPR </li></ul><ul><li>Sin QPR = Opp = 6 </li></ul><ul><li> Hyp 7 </li></ul><ul><li> </li></ul><ul><li>Sin QPR = 0.857 </li></ul><ul><li>QPR = Sinˉ¹0.857 </li></ul><ul><li>QPR = 59º </li></ul>7m 6m Q R P
9. 9. Example 3 <ul><li>Find angle RQP </li></ul><ul><li>Cos RQP = Adj = 6 </li></ul><ul><li> Hyp 7 </li></ul><ul><li>Cos RQP = 0.857 </li></ul><ul><li>RQP = Cosˉ¹0.857 </li></ul><ul><li>RQP = 31º </li></ul>7m 6m Q P R
10. 10. Example 3 <ul><li>RQP = 31° PQ = 7m </li></ul><ul><li>Sin RQP = Opp = PR </li></ul><ul><li> Hyp PQ </li></ul><ul><li>Sin 31° = PR </li></ul><ul><li> 7 </li></ul><ul><li>PR = 7 x Sin 31° 7 x 0.515 </li></ul><ul><li>PR = 3.6m </li></ul>
11. 11. Lesson Objectives <ul><li>Calculate the value of angles in a right angled triangle using trigonometric ratios. </li></ul><ul><li>Apply trigonometry to perform calculation checks. </li></ul><ul><li>Calculate the length of a side in a right angled triangle using trigonometric ratios. </li></ul>